Sorry, I don't really understand. Gpeasy is different from other CMS and web tech tools I've used. Can you be so specific as to tell me 'where to click' :)
I have installed the plugin. I am not really sure, where I find a 'section' or how I add a new one. Also, what is the purpose of ckeditor? It seems that I can edit a JSON-file there. Should I edit the JSON file in order to add the new 'free mail form'-section?

The instructions for adding a new content section in gpEasy differ a bit depending on the version you're using. Assuming you're using the latest release:

Right click over the content area of your current page and click the "Manage Sections" link. You can alternatively find the "Manage Sections" link in the admin toolbar under "Current Page" > "Editable Areas"

An editing window will open displaying current content sections and options for adding new sections. Select the 'free mail form' section and click "Add Section"